Milan were dominated by a young Gunners' team, but were able to keep the hosts from finding a way past their Australian goalkeeper Zeljko Kalac.
But Ancelotti admitted: "This is not a result that can give us tranquility. We struggled a bit and could have done more, but Arsenal are a strong side.
"We know we'll be under pressure as well in the second leg, but hope to go through anyway.
"As the Arsenal defence was quite high, we used Pato in a bid to let his pace cause them problems. They move the ball around very well in midfield, but also leave spaces."
Paolo Maldini proved magnificent against the much younger Gunners, especially after Alessandro Nesta's injury moved his position.
"Maldini did very well on the left and especially in the centre, where he is more comfortable and cleared many dangerous opportunities," added Ancelotti.